Intermediate chemistry
See also: and Spatial_structure_of_the_electron The first pair of electrons fall into the ground shell. Once that shell is filled no more electrons can go into it. Any additional electrons go into higher shells. The nucleus however works differently. The first few neutrons form the first shell. But any additional neutrons continue to fall into that same shell which continues to expand until there are 49 pairs of neutrons in that shell. :The highest energy gamma rays emitted by nuclei are around 10 Mev which corresponds to a wavelength of 124 fm. The electric force between two electrons is times stronger than the gravitational force. (12,242 * 2128) The energy required to assemble a sphere of uniform charge density = \frac{3}{5}\frac{Q^2}{4 \pi \epsilon_0 r} :For Q=1 electron charge and r=1.8506 angstrom thats . That energy is stored in the electric field of the electron. :The energy per volume stored in an electric field is proportional to the square of the field strength so twice the charge has 4 times as much energy. ::4*4.669 = 18.676. Mass of electron = Me = 510,999 ev Mass of proton = Mp = 938,272,000 ev Mass of neutron = Mn = 939,565,000 ev :Mn = Mp + Me + 782,300 ev Mass of muon = Mμ = 105.658 ev = 206.7683 * Me Mass of helium atom = 3,728,400,000 = 4*Me+4*Mp -52.31 Me :The missing 52.31 electron masses of energy is called the mass deficit or nuclear binding energy. Fusing hydrogen into helium releases this energy. Iron can be fused into heavier elements too but doing so consumes energy rather than releases energy. The total outward force for a solid 4-dimensional sphere of uniform density in Clifford rotation is \frac{4}{5} \cdot \frac{m v^2}{r} The angular momentum of a solid 4-dimensional sphere of uniform density is \frac{2}{3} \cdot mvr Empirically determined values for the size of atoms: :Diatomic Hydrogen (Z=2) = 1.9002 angstroms :Helium (Z=2) = 1.8506 angstroms In 3 dimensions the force between 2 electrons is: :: F = \frac{1}{4\pi\varepsilon_0} { e_1 e_2 \over r^2} :where m''e is the electron's mass, ''e1 is the charge of the electron, :: \varepsilon_0 = \frac{1}{180.95} \frac{e^2}{\text{eV} Å} :but in 4 dimensions: :: \varepsilon = \frac{2 \varepsilon_0}{\pi r} :where r is the distance at which the inverse square law gives the same result as the inverse cube law. In other words, the distance at which the inverse square law of the macroscopic world gives way to the inverse cube law of the microscopic world. The angular momentum is: :: \frac{2}{3} \cdot m_\mathrm{e} v r = \hbar :where ħ is reduced Planck constant :: \hbar= = 1.054\ 571\ 800(13)\times 10^{-34}\text{J}{\cdot}\text{s} :Therefore: :: v = \frac{3}{2} \cdot \frac{\hbar}{m_\mathrm{e}} \frac{1}{r} Back to top Density and thermal expansion Densities: :Crystalline solids: 1.2 :Amorphous solids: 1.1 :liquids: 1 Water ice is an exception. Ice has a density of 0.9167 From Wikipedia:Thermal expansion Thermal expansion generally decreases with increasing bond energy, which also has an effect on the melting point of solids, so, high melting point materials are more likely to have lower thermal expansion. In general, liquids expand slightly more than solids. The thermal expansion of glasses is higher compared to that of crystals. For an ideal gas, the volumetric thermal expansion (i.e., relative change in volume due to temperature change) depends on the type of process in which temperature is changed. Two simple cases are where the pressure is held constant (Isobaric process), or when the volume (Isochoric process) is held constant. The derivative of the ideal gas law, PV = T , is : P dV + V dP = dT where P is the pressure, V is the specific volume, and T is temperature measured in energy units. By definition of an isobaric thermal expansion, we have dP=0 , so that P dV=dT , and the isobaric thermal expansion coefficient is : \alpha_{P = C^{te}} \equiv \frac{1}{V} \left(\frac{d V}{d T}\right) = \frac{1}{V} \left(\frac{1}{P}\right) = \frac{1}{PV} = \frac{1}{T} . Similarly, if the volume is held constant, that is if dV=0 , we have V dP=dT , so that the isovolumic thermal expansion is : \alpha_{V=C^{te}} \equiv \frac{1}{P} \left(\frac{d P}{d T}\right) = \frac{1}{P} \left(\frac{1}{V}\right) = \frac{1}{P V} = \frac{1}{T} . For a solid, we can ignore the effects of pressure on the material, and the volumetric thermal expansion coefficient can be written: : \alpha_V = \frac{1}{V}\,\frac{dV}{dT} where V is the volume of the material, and dV/dT is the rate of change of that volume with temperature. This means that the volume of a material changes by some fixed fractional amount. For example, a steel block with a volume of 1 cubic meter might expand to 1.002 cubic meters when the temperature is raised by 50 K. This is an expansion of 0.2%. If we had a block of steel with a volume of 2 cubic meters, then under the same conditions, it would expand to 2.004 cubic meters, again an expansion of 0.2%. The volumetric expansion coefficient would be 0.2% for 50 K, or 0.004% K−1. If we already know the expansion coefficient, then we can calculate the change in volume : \frac{\Delta V}{V} = \alpha_V\Delta T where \Delta V/V is the fractional change in volume (e.g., 0.002) and \Delta T is the change in temperature (50 °C). For common materials like many metals and compounds, the thermal expansion coefficient is inversely proportional to the melting point. In particular for metals the relation is: : \alpha \approx \frac{0.020}{M_P} for halides and oxides : \alpha \approx \frac{0.038}{M_P} - 7.0 \cdot 10^{-6} \, \mathrm{K}^{-1} Back to top References Category:Intermediate chemistry